The government in the US is a what kind of democracy?

The United States is often called a "representative democracy", and a "democratic republic".

The United States is certainly not a pure democracy. On a national level, policy is never directly decided by a popular vote. Instead, legislation is effected by representatives, with representation being through a largely federal system; much power is invested in a President, who is not directly elected, with his Electors being allocated through a federal system; contests over the meaning of the law are settled by judges who are appointed by the President with the approval of the national legislators.

The US Constitution prevents representation perfectly proportional to population, unless the population is equally spread amongst the states, because the Constitution forbids any Amendments which would reduce equal representation of the states in the Senate. But, none-the-less, it's at least theoretically possible for the voters to make choices amongst candidates so that the legislature, President, and judges reached pretty much the same decisions that a pure democracy would.

The Word "republic" is rather vague. it can refer to any sort of government which is not a monarchy, but it generally refers to a system of government with a formal constitution in which a popular vote plays a significant role in decision-making. Calling the United States a "democratic republic" emphasizes that last idea.